Why is it that Sunni Islam does not follow adalat in its sources of authority unlike Shi’a?

In Sunni Islam, the main sources of authority are the Quran (Islam's holy book) and the Sunnah (the traditions of the Prophet Muhammad). The Sunnah is largely derived from Hadith (written collections of the sayings and actions of the Prophet Muhammad) and synthesised through the interpretation of learned scholars of Islam. These are the primary sources of authority and are rigourously checked for their authenticity. There is a strong preference to follow only what is contained in the Quran & Sunnah, in order to prevent alterations to the religion. There are 6 main articles of Faith in Sunni Islam: Belief in God, His Angels, His holy books, His Prophets, the Afterlife and Predestination (Qadr).
Shia Islam has 5 roots of religion: oneness of God, Justice of God (adalah), Prophethood, Leadership and Resurrection.
I hope that helps!